Abstract : A partial algebra is subdirectly covered, if it is represented as homomorphic image if a subdirect product, subject to certain uniqueness restrictions. A complete characterization of such representations is obtained in this paper. As important tool of this research the concept of 'weak homomorphism' is introduced. This is an extension of the usual concept of (partial) homomorphism to multi-valued mappings. Well-known results on homomorphisms are generalized accordingly. The approach and methods of this research originated in a study of automata decompositions and the results are applicable to the synthesis of automata (sequential machines). (Author)